Fig. REF (a) illustrates the effect of freely rotating surface dipoles on membrane interactions. The solid curves show the separation dependence of the disjoining pressure (REF ) computed from the numerical solution of the ZPB Eq. (REF ) for different values of the dipolar cation valency \(Q_+\) . One sees that in the standard case of purely monopolar charged membranes (black curve for \(Q_+=0\) ), the approach of the membranes leads to the monotonous rise of the uniformly repulsive pressure (\(d\downarrow P\uparrow \) ) according to the DH law [1]}
\(\beta P\approx 2\pi \ell _{\rm B}\sigma _{\rm s}^2Q_-^2\frac{\cosh ^2\left(\kappa _{\rm s}p\right)}{\sinh ^2\left(\kappa _{\rm s}d/2\right)}\) 
